FIA NLS Models: Biomass Growth vs. Biomass
JAH
2023-07-12
Background
This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement intervals (FIA re-measurement period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(tau\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(G\) with increasing \(B\), thus, weighted nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {mean B_{t1}}\) in equal-sample sized plot biomass bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is used to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine if including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) is warranted:
model 1: simple tau model \(G = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 2: tau-alpha model \(G = (1 + (yr-1990)* \tau/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)
sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot-based filtering criteria:
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile thresholding approach. We also calculated plot \(G_{TI}\) using as summed tree incremental growth for all trees > 12.5 cm (5 inches) (see supplementary methods). We use the difference between the two methods, which we define \(diff_G\) as the difference between the two methods \(G_{MB} - G_{TI}\) to identify erroneous or outlier growth calculations. We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1760 observations.
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6528 6446.0
## 2 6527 6168.5 1 277.57 293.7 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 26044.32
## 2 2 25758.85##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.19616 0.17071 1.149 0.251
## alpha -0.63021 0.03446 -18.286 < 2e-16 ***
## A 3.54580 0.12577 28.192 < 2e-16 ***
## k 6.08478 0.97267 6.256 4.21e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9721 on 6527 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 1.079e-06
## (353 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6527 6168.5
## 2 6526 6165.4 1 3.0319 3.2092 0.07327 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 25758.85
## 2 2a 25757.64
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.18836 0.17032 1.106 0.269
## alpha 0.62749 0.03454 18.168 <2e-16 ***
## A 3.79577 0.24275 15.636 <2e-16 ***
## k 70.36150 59.12289 1.190 0.234
## p 0.69559 0.04706 14.781 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.972 on 6526 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 8.494e-06
## (353 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.## Warning: Removed 26 rows containing missing values (`geom_point()`).## Warning: Removed 1038 rows containing missing values (`geom_line()`).
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18496 19634
## 2 18495 18485 1 1149 1149.6 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 69051.88
## 2 2 67938.32##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.38955 0.17879 7.772 8.13e-15 ***
## alpha -0.81312 0.02198 -36.993 < 2e-16 ***
## A 2.49608 0.07001 35.655 < 2e-16 ***
## k 11.16662 0.50650 22.046 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9997 on 18495 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.175e-06
## (4186 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18495 18485
## 2 18494 18441 1 44.079 44.2067 3.037e-11 ***
## 3 18494 18438 0 0.000
## 4 18493 18438 1 0.023 0.0235 0.8781
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 67938.32
## 2 2a 67896.16
## 3 2b 67892.98
## 4 2c 67894.96##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.35712 0.17684 7.674 1.75e-14 ***
## alpha 0.81019 0.02203 36.773 < 2e-16 ***
## A 3.13642 0.20040 15.651 < 2e-16 ***
## k 19.51596 4.10501 4.754 2.01e-06 ***
## s 0.58373 0.05366 10.879 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9985 on 18494 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 8.771e-06
## (4186 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 1889 rows containing missing values (`geom_point()`).## Warning: Removed 1031 rows containing missing values (`geom_line()`).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6938 9391.8
## 2 6937 8982.7 1 409.15 315.97 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 30727.86
## 2 2 30420.69##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.67555 0.13143 -5.140 2.82e-07 ***
## alpha -0.74229 0.03917 -18.950 < 2e-16 ***
## A 5.35702 0.19707 27.183 < 2e-16 ***
## k 23.62690 2.78246 8.491 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.138 on 6937 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.47e-06
## (366 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 30420.69
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.67555 0.13143 -5.140 2.82e-07 ***
## alpha -0.74229 0.03917 -18.950 < 2e-16 ***
## A 5.35702 0.19707 27.183 < 2e-16 ***
## k 23.62690 2.78246 8.491 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.138 on 6937 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.47e-06
## (366 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 31 rows containing missing values (`geom_point()`).## Warning: Removed 1036 rows containing missing values (`geom_line()`).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4746 5808.2
## 2 4745 5533.6 1 274.52 235.4 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 19696.25
## 2 2 19468.31##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.16997 0.23340 0.728 0.467
## alpha -0.76634 0.04579 -16.737 <2e-16 ***
## A 4.26363 0.20256 21.049 <2e-16 ***
## k 21.25535 1.77327 11.987 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.08 on 4745 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.14e-06
## (1097 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4745 5533.6
## 2 4744 5444.3 1 89.341 77.849 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 19468.31
## 2 2a 19393.01
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.03824 0.22050 0.173 0.8623
## alpha 0.75920 0.04542 16.714 < 2e-16 ***
## A 8.42134 1.45931 5.771 8.39e-09 ***
## k 317.27298 110.77065 2.864 0.0042 **
## p 0.22857 0.03088 7.401 1.59e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.071 on 4744 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.202e-06
## (1097 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 488 rows containing missing values (`geom_point()`).## Warning: Removed 1053 rows containing missing values (`geom_line()`).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8496 10221.3
## 2 8495 9933.6 1 287.73 246.06 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 34871.18
## 2 2 34630.50##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.59402 0.12174 -4.879 1.08e-06 ***
## alpha -0.67655 0.04042 -16.738 < 2e-16 ***
## A 5.14680 0.18549 27.748 < 2e-16 ***
## k 42.04611 3.37270 12.467 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.081 on 8495 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.908e-06
## (1507 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 2 34630.5
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.59402 0.12174 -4.879 1.08e-06 ***
## alpha -0.67655 0.04042 -16.738 < 2e-16 ***
## A 5.14680 0.18549 27.748 < 2e-16 ***
## k 42.04611 3.37270 12.467 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.081 on 8495 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.908e-06
## (1507 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 612 rows containing missing values (`geom_point()`).## Warning: Removed 1127 rows containing missing values (`geom_line()`).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12213 25243
## 2 12212 22266 1 2977.6 1633.1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 61285.28
## 2 2 59754.04##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.7192 0.1924 8.937 < 2e-16 ***
## alpha -0.8762 0.0195 -44.929 < 2e-16 ***
## A 3.8181 0.1117 34.191 < 2e-16 ***
## k 2.5595 0.3934 6.506 8.03e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.35 on 12212 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.642e-06
## (628 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_231, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12212 22266
## 2 12211 22265 1 0.89592 0.4914 0.4833
## model AIC
## 1 2 59754.04
## 2 2a NA
## 3 2b 59755.55
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.7192 0.1924 8.937 < 2e-16 ***
## alpha -0.8762 0.0195 -44.929 < 2e-16 ***
## A 3.8181 0.1117 34.191 < 2e-16 ***
## k 2.5595 0.3934 6.506 8.03e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.35 on 12212 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.642e-06
## (628 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: fits
- add s+p model: does not fit
predict and plot
## Warning: Removed 121 rows containing missing values (`geom_point()`).## Warning: Removed 1017 rows containing missing values (`geom_line()`).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12486 31324
## 2 12485 27933 1 3390.8 1515.6 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 63593.26
## 2 2 62164.41##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.3894 0.2016 6.89 5.85e-12 ***
## alpha -0.8713 0.0198 -44.01 < 2e-16 ***
## A 3.9059 0.1289 30.30 < 2e-16 ***
## k 6.3334 0.5191 12.20 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.496 on 12485 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.065e-06
## (678 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12485 27933
## 2 12484 27900 1 33.550 15.012 0.0001074 ***
## 3 12484 27908 0 0.000
## 4 12483 27894 1 14.491 6.485 0.0108905 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 62164.41
## 2 2a 62151.40
## 3 2b 62155.33
## 4 2c 62150.84##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.37237 0.20054 6.843 8.10e-12 ***
## alpha 0.87172 0.01979 44.055 < 2e-16 ***
## A 3.89136 0.14849 26.207 < 2e-16 ***
## k 26.06148 4.92503 5.292 1.23e-07 ***
## s 1.60320 0.40302 3.978 6.99e-05 ***
## p 0.54938 0.06617 8.302 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.495 on 12483 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.389e-06
## (678 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 153 rows containing missing values (`geom_point()`).## Warning: Removed 953 rows containing missing values (`geom_line()`).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1274 2866.7
## 2 1273 2700.1 1 166.61 78.548 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6409.271
## 2 2 6334.811##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.8095 0.6929 1.168 0.24289
## alpha -0.7606 0.0775 -9.814 < 2e-16 ***
## A 3.9836 0.5071 7.856 8.39e-15 ***
## k 3.7233 1.3736 2.711 0.00681 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.456 on 1273 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.333e-06
## (67 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1273 2700.1
## 2 1272 2697.6 1 2.5536 1.2041 0.2727
## model AIC
## 1 2 6334.811
## 2 2a 6335.603
## 3 2b 6334.990
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.8095 0.6929 1.168 0.24289
## alpha -0.7606 0.0775 -9.814 < 2e-16 ***
## A 3.9836 0.5071 7.856 8.39e-15 ***
## k 3.7233 1.3736 2.711 0.00681 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.456 on 1273 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.333e-06
## (67 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
predict and plot
## Warning: Removed 22 rows containing missing values (`geom_point()`).## Warning: Removed 948 rows containing missing values (`geom_line()`).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 76 136.79
## 2 75 125.36 1 11.426 6.836 0.01079 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 421.2541
## 2 2 416.3630##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.9701 1.7313 -0.560 0.57692
## alpha -0.9705 0.3345 -2.901 0.00488 **
## A 9.7517 4.4803 2.177 0.03266 *
## k 20.9759 15.5170 1.352 0.18050
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.293 on 75 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.047e-06
## (6 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_242, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 416.363
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.9701 1.7313 -0.560 0.57692
## alpha -0.9705 0.3345 -2.901 0.00488 **
## A 9.7517 4.4803 2.177 0.03266 *
## k 20.9759 15.5170 1.352 0.18050
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.293 on 75 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.047e-06
## (6 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 2 rows containing missing values (`geom_point()`).## Warning: Removed 725 rows containing missing values (`geom_line()`).
plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1740 2174.3
## 2 1739 2160.3 1 14.052 11.312 0.0007869 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7121.686
## 2 2 7112.386##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4136 0.4550 0.909 0.363521
## alpha -0.3868 0.1103 -3.506 0.000467 ***
## A 3.4066 0.3072 11.088 < 2e-16 ***
## k 19.8898 3.6894 5.391 7.96e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.115 on 1739 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.963e-06
## (547 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 7112.386
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4136 0.4550 0.909 0.363521
## alpha -0.3868 0.1103 -3.506 0.000467 ***
## A 3.4066 0.3072 11.088 < 2e-16 ***
## k 19.8898 3.6894 5.391 7.96e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.115 on 1739 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.963e-06
## (547 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 249 rows containing missing values (`geom_point()`).## Warning: Removed 1176 rows containing missing values (`geom_line()`).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 639 1515.9
## 2 638 1458.2 1 57.633 25.215 6.662e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2995.098
## 2 2 2972.213##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4255 0.9432 0.451 0.652
## alpha -0.7802 0.1391 -5.609 3.03e-08 ***
## A 2.8095 0.5085 5.525 4.82e-08 ***
## k 1.8978 2.2196 0.855 0.393
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.512 on 638 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.496e-06
## (72 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_255, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 638 1458.2
## 2 637 1457.0 1 1.1985 0.524 0.4694
## model AIC
## 1 2 2972.213
## 2 2a NA
## 3 2b 2973.686
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4255 0.9432 0.451 0.652
## alpha -0.7802 0.1391 -5.609 3.03e-08 ***
## A 2.8095 0.5085 5.525 4.82e-08 ***
## k 1.8978 2.2196 0.855 0.393
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.512 on 638 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.496e-06
## (72 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91522, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.246, p-value = 2.177e-05
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 22 rows containing missing values (`geom_point()`).## Warning: Removed 1235 rows containing missing values (`geom_line()`).
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
note: model fit, but fit was funky due to data being sparse
predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 203 98.779
## 2 202 94.169 1 4.6095 9.8877 0.001915 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 474.7048
## 2 2 466.8603##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.3054 0.8972 -1.455 0.147197
## alpha -0.8771 0.2465 -3.559 0.000464 ***
## A 5.1018 1.7192 2.968 0.003365 **
## k 144.9621 49.7005 2.917 0.003938 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6828 on 202 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.054e-06
## (12 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 202 94.169
## 2 201 93.989 1 0.18070 0.3864 0.5349
## 3 201 94.111 0 0.00000
## 4 200 93.424 1 0.68623 1.4691 0.2269
## model AIC
## 1 2 466.8603
## 2 2a 468.4646
## 3 2b 468.7317
## 4 2c 469.2240##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.3054 0.8972 -1.455 0.147197
## alpha -0.8771 0.2465 -3.559 0.000464 ***
## A 5.1018 1.7192 2.968 0.003365 **
## k 144.9621 49.7005 2.917 0.003938 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6828 on 202 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.054e-06
## (12 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 1 rows containing missing values (`geom_point()`).## Warning: Removed 1103 rows containing missing values (`geom_line()`).
plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Error in nls(fg_1, data = G_331, start = c(tau = tau.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(tau = tau.start, alpha = alpha.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not foundsummary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 187 155.51
## 2 186 150.63 1 4.8775 6.0228 0.01504 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 631.7909
## 2 2 627.7361##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.7899 1.6302 0.485 0.62858
## alpha -0.6637 0.2468 -2.689 0.00781 **
## A 3.8735 1.2352 3.136 0.00199 **
## k 59.6114 18.8470 3.163 0.00182 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8999 on 186 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.995e-06
## (42 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 186 150.63
## 2 185 147.85 1 2.7851 3.485 0.06351 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 627.7361
## 2 2a 626.1902
## 3 2b 627.0534
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.81595 1.62271 0.503 0.61568
## alpha 0.66637 0.23893 2.789 0.00584 **
## A 5.12725 2.17868 2.353 0.01965 *
## k 147.54348 104.15313 1.417 0.15828
## p 0.10195 0.03947 2.583 0.01057 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.894 on 185 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.375e-06
## (42 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
predict and plot
## Warning: Removed 21 rows containing missing values (`geom_point()`).## Warning: Removed 1120 rows containing missing values (`geom_line()`).
plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 108 82.141
## 2 107 74.076 1 8.0648 11.649 0.0009079 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 317.2803
## 2 2 307.8092##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.9433 5.4470 0.357 0.721976
## alpha -0.9851 0.2476 -3.978 0.000127 ***
## A 3.2731 2.7047 1.210 0.228900
## k 82.5474 33.3159 2.478 0.014786 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.832 on 107 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.997e-06
## (13 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 107 74.076
## 2 106 74.076 1 0.000125 0.0002 0.9894
## 3 106 74.067 0 0.000000
## 4 105 73.977 1 0.090103 0.1279 0.7213
## model AIC
## 1 2 307.8092
## 2 2a 309.8090
## 3 2b 309.7950
## 4 2c 311.6599##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.9433 5.4470 0.357 0.721976
## alpha -0.9851 0.2476 -3.978 0.000127 ***
## A 3.2731 2.7047 1.210 0.228900
## k 82.5474 33.3159 2.478 0.014786 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.832 on 107 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.997e-06
## (13 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 4 rows containing missing values (`geom_point()`).## Warning: Removed 1241 rows containing missing values (`geom_line()`).
plotting 2
411 - Everglades
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6431 5529.0
## 2 6430 5196.9 1 332.1 410.91 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24631.49
## 2 2 24234.93##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.81749 0.21414 3.818 0.000136 ***
## alpha -0.64323 0.02951 -21.793 < 2e-16 ***
## A 2.96500 0.11944 24.823 < 2e-16 ***
## k 1.87319 0.87956 2.130 0.033236 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.899 on 6430 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.313e-06
## (344 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M211, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6430 5196.9
## 2 6429 5190.8 1 6.1004 7.5556 0.005999 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 24234.93
## 2 2a NA
## 3 2b 24229.38
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.80341 0.21262 3.779 0.000159 ***
## alpha 0.64462 0.02947 21.877 < 2e-16 ***
## A 2.92914 0.11295 25.933 < 2e-16 ***
## k 15.35544 3.85224 3.986 6.79e-05 ***
## s 4.27661 2.19938 1.944 0.051884 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8986 on 6429 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 6.485e-06
## (344 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: fits
- add s+p model: does not fit
predict and plot
## Warning: Removed 9 rows containing missing values (`geom_point()`).## Warning: Removed 1108 rows containing missing values (`geom_line()`).
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7778 13858
## 2 7777 13518 1 339.94 195.57 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 36650.46
## 2 2 36459.21##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.40077 0.18831 2.128 0.0333 *
## alpha -0.81726 0.05533 -14.770 < 2e-16 ***
## A 4.31613 0.18952 22.774 < 2e-16 ***
## k 26.44060 3.72512 7.098 1.38e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.318 on 7777 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 9.35e-06
## (405 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 36459.21
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.40077 0.18831 2.128 0.0333 *
## alpha -0.81726 0.05533 -14.770 < 2e-16 ***
## A 4.31613 0.18952 22.774 < 2e-16 ***
## k 26.44060 3.72512 7.098 1.38e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.318 on 7777 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 9.35e-06
## (405 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 27 rows containing missing values (`geom_point()`).## Warning: Removed 982 rows containing missing values (`geom_line()`).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 843 1270.5
## 2 842 1225.9 1 44.684 30.692 4.045e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3539.637
## 2 2 3511.349##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.1536 1.6195 1.947 0.0518 .
## alpha -0.9337 0.1549 -6.029 2.47e-09 ***
## A 2.1122 0.4820 4.382 1.33e-05 ***
## k 26.3827 11.7080 2.253 0.0245 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.207 on 842 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.981e-06
## (47 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223, :
## singular gradient
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 3511.349
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.1536 1.6195 1.947 0.0518 .
## alpha -0.9337 0.1549 -6.029 2.47e-09 ***
## A 2.1122 0.4820 4.382 1.33e-05 ***
## k 26.3827 11.7080 2.253 0.0245 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.207 on 842 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.981e-06
## (47 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 1 rows containing missing values (`geom_point()`).## Warning: Removed 1175 rows containing missing values (`geom_line()`).
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 952 1446.6
## 2 951 1370.3 1 76.287 52.943 7.178e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4071.286
## 2 2 4021.547##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 5.5388 2.8452 1.947 0.05186 .
## alpha -0.8352 0.1063 -7.857 1.06e-14 ***
## A 1.5900 0.4566 3.482 0.00052 ***
## k 13.1811 4.8742 2.704 0.00697 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.2 on 951 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 9.536e-06
## (54 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 4021.547
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 5.5388 2.8452 1.947 0.05186 .
## alpha -0.8352 0.1063 -7.857 1.06e-14 ***
## A 1.5900 0.4566 3.482 0.00052 ***
## k 13.1811 4.8742 2.704 0.00697 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.2 on 951 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 9.536e-06
## (54 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95392, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.8203, p-value = 1.434e-06
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 8 rows containing missing values (`geom_point()`).## Warning: Removed 1218 rows containing missing values (`geom_line()`).
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3129 8568.5
## 2 3128 8205.0 1 363.57 138.6 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 16100.13
## 2 2 15966.34##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.65365 0.25317 -6.532 7.55e-11 ***
## alpha -0.94510 0.07264 -13.010 < 2e-16 ***
## A 10.91594 0.93800 11.637 < 2e-16 ***
## k 104.82478 8.83904 11.859 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.62 on 3128 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 5.362e-06
## (171 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3128 8205.0
## 2 3127 8163.5 1 41.421 15.866 6.954e-05 ***
## 3 3127 8181.8 0 0.000
## 4 3126 8126.6 1 55.197 21.232 4.231e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 15966.34
## 2 2a 15952.49
## 3 2b 15959.48
## 4 2c 15940.28##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.65297 0.25162 -6.569 5.90e-11 ***
## alpha 0.93030 0.07283 12.774 < 2e-16 ***
## A 9.21087 0.78875 11.678 < 2e-16 ***
## k 140.22607 9.54888 14.685 < 2e-16 ***
## p 0.32457 0.03009 10.786 < 2e-16 ***
## s 2.60360 0.44461 5.856 5.24e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.612 on 3126 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.473e-06
## (171 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 39 rows containing missing values (`geom_point()`).## Warning: Removed 126 rows containing missing values (`geom_line()`).
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1657 3824.4
## 2 1656 3744.5 1 79.903 35.337 3.375e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7969.307
## 2 2 7936.257##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.8503 0.3242 -5.707 1.36e-08 ***
## alpha -0.7145 0.1114 -6.412 1.87e-10 ***
## A 13.9898 1.6309 8.578 < 2e-16 ***
## k 193.1434 23.7409 8.135 7.97e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.504 on 1656 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.696e-06
## (333 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1656 3744.5
## 2 1655 3740.7 1 3.8563 1.7062 0.1917
## 3 1655 3740.8 0 0.0000
## 4 1654 3740.6 1 0.1691 0.0748 0.7845
## model AIC
## 1 2 7936.257
## 2 2a 7936.547
## 3 2b 7936.589
## 4 2c 7938.514##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.8503 0.3242 -5.707 1.36e-08 ***
## alpha -0.7145 0.1114 -6.412 1.87e-10 ***
## A 13.9898 1.6309 8.578 < 2e-16 ***
## k 193.1434 23.7409 8.135 7.97e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.504 on 1656 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.696e-06
## (333 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 149 rows containing missing values (`geom_point()`).
plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 347 171.17
## 2 346 151.29 1 19.881 45.47 6.515e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 858.0286
## 2 2 816.8144##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.2907 0.2919 -7.847 5.39e-14 ***
## alpha -0.8298 0.1085 -7.647 2.06e-13 ***
## A 10.2668 1.9746 5.200 3.43e-07 ***
## k 170.6425 42.6923 3.997 7.84e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6612 on 346 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.574e-06
## (17 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 346 151.29
## 2 345 150.77 1 0.51884 1.1872 0.2766
## 3 345 150.87 0 0.00000
## 4 344 150.70 1 0.17087 0.3900 0.5327
## model AIC
## 1 2 816.8144
## 2 2a 817.6120
## 3 2b 817.8562
## 4 2c 819.4596##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.2907 0.2919 -7.847 5.39e-14 ***
## alpha -0.8298 0.1085 -7.647 2.06e-13 ***
## A 10.2668 1.9746 5.200 3.43e-07 ***
## k 170.6425 42.6923 3.997 7.84e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6612 on 346 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.574e-06
## (17 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 1183 rows containing missing values (`geom_line()`).
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1671 1536.0
## 2 1670 1440.7 1 95.321 110.49 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4833.233
## 2 2 4727.986##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.71205 0.60194 -1.183 0.237
## alpha -0.70634 0.05683 -12.429 < 2e-16 ***
## A 2.60054 0.41890 6.208 6.75e-10 ***
## k 45.32243 7.61770 5.950 3.27e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9288 on 1670 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.252e-06
## (83 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1670 1440.7
## 2 1669 1425.2 1 15.487 18.136 2.171e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 4727.986
## 2 2a 4711.894
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.65228 0.61486 -1.061 0.2889
## alpha 0.71340 0.05595 12.751 <2e-16 ***
## A 7.10119 4.82364 1.472 0.1412
## k 638.51092 642.93098 0.993 0.3208
## p 0.11674 0.06709 1.740 0.0821 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9241 on 1669 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.73e-06
## (83 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 7 rows containing missing values (`geom_point()`).## Warning: Removed 1091 rows containing missing values (`geom_line()`).
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2489 2883.3
## 2 2488 2629.0 1 254.37 240.73 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8699.173
## 2 2 8471.019##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.83974 0.43909 -1.912 0.0559 .
## alpha -0.90282 0.05006 -18.036 < 2e-16 ***
## A 4.58341 0.56859 8.061 1.16e-15 ***
## k 61.59170 6.83813 9.007 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.028 on 2488 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 9.108e-06
## (129 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2488 2629.0
## 2 2487 2546.1 1 82.903 80.98 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 8471.019
## 2 2a 8393.170
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.88809 0.41840 -2.123 0.033885 *
## alpha 0.88744 0.04965 17.873 < 2e-16 ***
## A 13.08533 4.76063 2.749 0.006027 **
## k 661.38696 325.80525 2.030 0.042462 *
## p 0.08484 0.02516 3.371 0.000759 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.012 on 2487 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.975e-06
## (129 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 53 rows containing missing values (`geom_point()`).## Warning: Removed 1001 rows containing missing values (`geom_line()`).
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1663 2105.7
## 2 1662 1836.5 1 269.18 243.6 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6652.568
## 2 2 6426.703##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.63995 0.55842 -1.146 0.252
## alpha -0.94758 0.05301 -17.875 < 2e-16 ***
## A 5.64164 0.81725 6.903 7.21e-12 ***
## k 45.22933 5.02882 8.994 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.051 on 1662 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 8.953e-06
## (92 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1662 1836.5
## 2 1661 1748.7 1 87.841 83.437 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 6426.703
## 2 2a 6347.049
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.77897 0.50926 -1.530 0.126308
## alpha 0.93774 0.05149 18.211 < 2e-16 ***
## A 16.98105 6.18278 2.747 0.006088 **
## k 704.86254 347.68787 2.027 0.042793 *
## p 0.10435 0.03031 3.442 0.000591 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.026 on 1661 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.144e-06
## (92 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## Warning: Removed 25 rows containing missing values (`geom_point()`).## Warning: Removed 925 rows containing missing values (`geom_line()`).
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 343 334.98
## 2 342 308.64 1 26.333 29.179 1.238e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1054.269
## 2 2 1027.940##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.2716 1.0815 -0.251 0.80189
## alpha -0.8098 0.1322 -6.128 2.45e-09 ***
## A 2.6559 0.6651 3.993 7.98e-05 ***
## k 33.8809 10.6800 3.172 0.00165 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.95 on 342 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.796e-06
## (105 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 342 308.64
## 2 341 308.47 1 0.173247 0.1915 0.6619
## 3 341 308.40 0 0.000000
## 4 340 308.39 1 0.014347 0.0158 0.9000
## model AIC
## 1 2 1027.940
## 2 2a 1029.746
## 3 2b 1029.669
## 4 2c 1031.653##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.2716 1.0815 -0.251 0.80189
## alpha -0.8098 0.1322 -6.128 2.45e-09 ***
## A 2.6559 0.6651 3.993 7.98e-05 ***
## k 33.8809 10.6800 3.172 0.00165 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.95 on 342 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.796e-06
## (105 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
predict and plot
## Warning: Removed 42 rows containing missing values (`geom_point()`).## Warning: Removed 1264 rows containing missing values (`geom_line()`).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 2a |
| 212 | Laurentian Mixed Forest | 2b |
| 221 | Eastern Broadleaf Forest | 2 |
| 222 | Midwest Broadleaf Forest | 2a |
| 223 | Central Interior Broadleaf Forest | 2 |
| 231 | Southeastern Mixed Forest | 2 |
| 232 | Outer Coastal Plain Mixed Forest | 2c |
| 234 | Lower Mississippi Riverine Forest | 2 |
| 242 | Pacific Lowland Mixed Forest | 2 |
| 251 | Prairie Parkland (Temperate) | 2 |
| 255 | Prairie Parkland (Subtropical) | 2 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | 2 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | 2a |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | 2 |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2b |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2 |
| M223 | Ozark Broadleaf Forest Meadow | 2 |
| M231 | Ouachita Mixed Forest | 2 |
| M242 | Cascade Mixed Forest | 2c |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 2a |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2a |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2a |
| M334 | Black Hills Coniferous Forest | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6884 | 2879 | 0.1883607 | 0.0290087 | -0.1455213 | 0.5222427 | 0.6274918 | 0.0011929 | 0.5597848 | 0.6951988 | 3.795766 | 3.3198881 | 4.271643 | 70.361497 | -45.538736 | 186.261731 |
| 212 | Laurentian Mixed Forest | east | 22685 | 9493 | 1.3571172 | 0.0312721 | 1.0104959 | 1.7037384 | 0.8101887 | 0.0004854 | 0.7670035 | 0.8533738 | 3.136415 | 2.7436151 | 3.529215 | 19.515960 | 11.469758 | 27.562163 |
| 221 | Eastern Broadleaf Forest | east | 7307 | 3560 | -0.6755457 | 0.0172735 | -0.9331864 | -0.4179050 | -0.7422922 | 0.0015343 | -0.8190780 | -0.6655063 | 5.357021 | 4.9706988 | 5.743343 | 23.626902 | 18.172427 | 29.081377 |
| 222 | Midwest Broadleaf Forest | east | 5846 | 2589 | 0.0382426 | 0.0486224 | -0.3940493 | 0.4705344 | 0.7592017 | 0.0020633 | 0.6701495 | 0.8482538 | 8.421344 | 5.5604167 | 11.282271 | 317.272977 | 100.111085 | 534.434868 |
| 223 | Central Interior Broadleaf Forest | east | 10006 | 3860 | -0.5940199 | 0.0148218 | -0.8326695 | -0.3553703 | -0.6765477 | 0.0016337 | -0.7557781 | -0.5973173 | 5.146801 | 4.7832031 | 5.510400 | 42.046115 | 35.434811 | 48.657418 |
| 231 | Southeastern Mixed Forest | east | 12844 | 5935 | 1.7191727 | 0.0370065 | 1.3420956 | 2.0962499 | -0.8762149 | 0.0003803 | -0.9144425 | -0.8379874 | 3.818098 | 3.5992055 | 4.036990 | 2.559496 | 1.788330 | 3.330662 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13167 | 6463 | 1.3723711 | 0.0402169 | 0.9792790 | 1.7654632 | 0.8717178 | 0.0003915 | 0.8329322 | 0.9105035 | 3.891356 | 3.6002987 | 4.182414 | 26.061483 | 16.407657 | 35.715308 |
| 234 | Lower Mississippi Riverine Forest | east | 1344 | 759 | 0.8095486 | 0.4801207 | -0.5498176 | 2.1689147 | -0.7606008 | 0.0060068 | -0.9126498 | -0.6085519 | 3.983594 | 2.9887786 | 4.978409 | 3.723276 | 1.028469 | 6.418082 |
| 242 | Pacific Lowland Mixed Forest | west | 85 | 85 | -0.9701074 | 2.9973158 | -4.4189856 | 2.4787708 | -0.9704833 | 0.1118949 | -1.6368554 | -0.3041112 | 9.751690 | 0.8264274 | 18.676952 | 20.975900 | -9.935584 | 51.887383 |
| 251 | Prairie Parkland (Temperate) | east | 2290 | 903 | 0.4135710 | 0.2070395 | -0.4788649 | 1.3060069 | -0.3868200 | 0.0121743 | -0.6032275 | -0.1704126 | 3.406591 | 2.8040034 | 4.009178 | 19.889791 | 12.653732 | 27.125849 |
| 255 | Prairie Parkland (Subtropical) | east | 714 | 318 | 0.4255101 | 0.8895754 | -1.4265887 | 2.2776089 | -0.7802093 | 0.0193453 | -1.0533335 | -0.5070851 | 2.809477 | 1.8108544 | 3.808100 | 1.897828 | -2.460867 | 6.256522 |
| 261 | California Coastal Chaparral Forest and Shrub | west | 26 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | west | 159 | 157 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | west | 218 | 218 | -1.3054454 | 0.8048950 | -3.0744441 | 0.4635532 | -0.8771256 | 0.0607386 | -1.3630742 | -0.3911770 | 5.101849 | 1.7119172 | 8.491781 | 144.962107 | 46.963721 | 242.960492 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | west | 331 | 255 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | west | 232 | 128 | 0.8159476 | 2.6331754 | -2.3854407 | 4.0173358 | 0.6663747 | 0.0570885 | 0.1949928 | 1.1377567 | 5.127250 | 0.8290002 | 9.425499 | 147.543476 | -57.937096 | 353.024047 |
| 341 | Intermountain Semi-Desert and Desert | west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | west | 124 | 123 | 1.9432557 | 29.6698155 | -8.8547877 | 12.7412991 | -0.9850791 | 0.0613271 | -1.4760025 | -0.4941556 | 3.273060 | -2.0887741 | 8.634895 | 82.547372 | 16.502570 | 148.592174 |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6778 | 3008 | 0.8034138 | 0.0452068 | 0.3866101 | 1.2202176 | 0.6446201 | 0.0008682 | 0.5868588 | 0.7023815 | 2.929143 | 2.7077264 | 3.150559 | 15.355443 | 7.803771 | 22.907115 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8186 | 3765 | 0.4007711 | 0.0354588 | 0.0316423 | 0.7698999 | -0.8172623 | 0.0030615 | -0.9257254 | -0.7087992 | 4.316127 | 3.9446096 | 4.687644 | 26.440600 | 19.138368 | 33.742832 |
| M223 | Ozark Broadleaf Forest Meadow | east | 893 | 348 | 3.1536219 | 2.6226423 | -0.0250255 | 6.3322692 | -0.9337355 | 0.0239854 | -1.2377165 | -0.6297546 | 2.112200 | 1.1660418 | 3.058359 | 26.382711 | 3.402327 | 49.363095 |
| M231 | Ouachita Mixed Forest | east | 1009 | 496 | 5.5387856 | 8.0950993 | -0.0447882 | 11.1223595 | -0.8352323 | 0.0112997 | -1.0438425 | -0.6266222 | 1.589979 | 0.6939600 | 2.485998 | 13.181124 | 3.615640 | 22.746607 |
| M242 | Cascade Mixed Forest | west | 3303 | 3286 | -1.6529736 | 0.0633113 | -2.1463255 | -1.1596216 | 0.9303037 | 0.0053036 | 0.7875131 | 1.0730943 | 9.210866 | 7.6643535 | 10.757379 | 140.226074 | 121.503360 | 158.948787 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | west | 1993 | 1828 | -1.8503008 | 0.1051331 | -2.4862690 | -1.2143326 | -0.7144990 | 0.0124187 | -0.9330755 | -0.4959224 | 13.989840 | 10.7910407 | 17.188639 | 193.143382 | 146.578088 | 239.708676 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | west | 367 | 367 | -2.2907012 | 0.0852283 | -2.8648995 | -1.7165028 | -0.8297544 | 0.0117744 | -1.0431762 | -0.6163326 | 10.266782 | 6.3831165 | 14.150447 | 170.642491 | 86.673365 | 254.611616 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | west | 1757 | 1757 | -0.6522770 | 0.3780549 | -1.8582584 | 0.5537044 | 0.7133954 | 0.0031300 | 0.6036633 | 0.8231276 | 7.101191 | -2.3598385 | 16.562221 | 638.510917 | -622.525139 | 1899.546973 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 2621 | 2611 | -0.8880933 | 0.1750560 | -1.7085356 | -0.0676510 | 0.8874392 | 0.0024653 | 0.7900755 | 0.9848030 | 13.085334 | 3.7501276 | 22.420540 | 661.386957 | 22.509468 | 1300.264447 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 1758 | 1747 | -0.7789660 | 0.2593496 | -1.7778326 | 0.2199007 | 0.9377412 | 0.0026516 | 0.8367420 | 1.0387404 | 16.981052 | 4.8541978 | 29.107907 | 704.862539 | 22.909901 | 1386.815177 |
| M334 | Black Hills Coniferous Forest | west | 451 | 179 | -0.2715511 | 1.1695390 | -2.3986862 | 1.8555841 | -0.8098118 | 0.0174641 | -1.0697448 | -0.5498788 | 2.655893 | 1.3477070 | 3.964080 | 33.880890 | 12.874075 | 54.887704 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | west | 220 | 220 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
parameter variance co-variance
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
plot alpha (biomass growth compensation effect)
plot A (asymptote of forest biomass growth in Mg/ha/yr)
## Warning: Removed 11 rows containing missing values (`geom_point()`).
plot k (stand biomass at half biomss G in Mg/ha)
## Warning: Removed 11 rows containing missing values (`geom_point()`).